What is the authenticity of punishing disobedient Muslims who are not polytheists, and does the promise of salvation from Allah's punishment in the Hadith of Mu'adh ibn Jabal include one who committed minor shirk, then repented and died upon Tawhid?

We have not come across a hadith with the narration mentioned by the dear brother in his question. Perhaps he combined two narrated hadiths. In the first hadith, from Mu'adh ibn Jabal (may Allah be pleased with him), it states that the right of Allah upon His servants is that they worship Him and not associate anything with Him, and the right of the servants upon Allah is that He does not punish whoever does not associate anything with Him. The phrase "even if he committed zina and even if he stole" is not mentioned in it. As for the second hadith, from Abu Dharr (may Allah be pleased with him), it states that whoever from his Ummah dies not associating anything with Allah will enter Paradise, "even if he committed zina and even if he stole," and the negation of punishment is not mentioned in it.

The scholars have differed in interpreting the negation of punishment for whoever dies not associating anything with Allah. The madhhab of Ahl al-Sunnah is that those who commit sins are subject to Allah's will, and whoever dies upon faith and Tawhid will enter Paradise, either directly through His Lord's mercy or after being punished for the disobedience they committed. The disobedient believers may be punished, or they may not be punished if they repent, or if Allah favors them with forgiveness.

The obligation is to distance oneself from shirk and all other sins, to repent from them, and to be sincere in doing so, so that the servant may hope for salvation from Allah's punishment.